The importance of safe and flexible disturbance rejection at high frequencies has been ever increasing in modern control systems. For example, the deployment of hard disk drives (HDD) in all-in-one desktop/laptop computers and in intelligent TVs requires that the HDD control system be robust to (e.g., have the ability to reject, attenuate) vibration disturbances that can occur at, for example, 5000 Hz and 6000 Hz, which capability has, thus far, been unattainable.
The disturbance observer (DOB) is a widely known feedback control technique. The basic operation of a DOB is based upon the known proposition that, for the servo control system, if the control command, the system output, and the is plant are known, then the disturbance in the system can be estimated. Because an inverse model of a conventional dynamic system is in general a non-causal system, delay terms are added in digital disturbance observers to make the inverse realizable. Because the inverse transfer function amplifies measurement noise, a low-pass or band-pass Q filter is used to improve the signal to noise ratio (SNR). The low-pass Q-filter approach intrinsically cannot help reject high-frequency disturbances since it is unable to estimate the high-frequency disturbances. Additionally, the DOB works to reject a disturbance d(k) by performing the operation d(k)−dest(k−m), where the subscript est denotes estimation and m represents the delay of the plant (in this case, a mechanical model of at least a portion of a hard disk drive, such as a model of an actuator arm actuated by a VCM). However, such solutions cannot meet the requirements in ultra-high frequency disturbance rejection (such as rejection of disturbances at 5000 and 6000 Hz, for example), since the m-step delay causes mismatched signal cancellation and even system instability at such high frequencies. Moreover, in DOBs equipped with band-pass Q filters, the designed center frequency of the Q filter does not align with that of the final error rejection curve (ERC), resulting in greatly increased tuning time and consequently increased product cost.
In FIG. 1, the delay factor m (computed from the identified model of the plant) is equal to 2, the sampling time in the control system Ts=3.75×10−5 sec, and the center frequency ω0 of the Q filter is 4000 Hz. It is observed that in the actual closed-loop ERC, disturbances at 4000 Hz are not attenuated but are, in fact, undesirably amplified due to this problematic frequency mismatch. In this example, it can be computed that the m=2 steps of delays translate to m×360×4000×Ts=108.108 degrees of phase lag during the disturbance cancellation d(k)−dest(k−m).
When hard disk drives are incorporated into consumer devices such as, for example, televisions, the tone noise from the TV's speakers or the entertainment system typically varies from about 20 Hz to about 16000 Hz (i.e., generally within the range of human hearing). However, when the tone noise sweeps above 3000 Hz, conventional DOB disturbance estimation and cancellation schemes do not have the capability to attenuate the resulting disturbance. Indeed, theoretical limitations prevent the conventional DOB scheme from being applied to environments is susceptible to ultra-high (e.g., 4000 Hz and above) frequency disturbance environments.
What are needed, therefore, are methods for accurately controlling hard disk drives that do not suffer from the aforementioned disadvantages and that are configured to function in the presence of ultra-high frequency disturbances.